Plinko odds: rows, risk levels and the binomial distribution
Why a Plinko ball usually lands near the middle: exact slot chances for 8 and 16 rows, what the risk levels change, and where the game comes from.
Fact-checked 18 October 2026 · 6 sourcesA Plinko ball bouncing down the pins looks chaotic, but where it lands follows one of the best-understood patterns in probability. Each row is a coin flip, and the slot is just the number of times the ball went right. That makes the chance of every slot exact, for any number of rows, before you even pick a risk level.
From a TV pegboard to a casino game
Plinko premiered on The Price Is Right on January 3, 1983. A contestant starts with one chip and can win up to four more by pricing small prizes, then drops them one at a time down a tall pegboard into nine slots at the bottom. Each chip can be worth up to $10,000, the value of the centre slot.
The board borrows a much older idea. Francis Galton designed a pegboard for a talk at the Royal Institution in 1874 and wrote about it in his 1889 book Natural Inheritance. Beads dropped into a Galton board, also called a bean machine or quincunx, bounce left or right off each peg and pile up in bins in a bell shape. Casino Plinko is a digital Galton board with a payout on each bin.
One coin flip per row
In the game, each row uses one float, a random number between 0 and 1 drawn from your bet's seed pair. Then floor(float × 2) gives 0 (left) or 1 (right), and the slot is the number of rights. A float below 0.5 means left and anything from 0.5 up means right, so every row is an exact 50/50, independent of the others.
With 8 rows the ball makes 8 left-or-right choices, so there are 2⁸ = 256 equally likely paths and 9 slots, numbered 0 to 8 from the left. Only one path reaches slot 0 (left every time), but 70 different paths reach slot 4 in the centre. The number of paths to slot k is the binomial coefficient C(n, k), the numbers in Pascal's triangle, and the chance of slot k is C(n, k) / 2ⁿ. That's the binomial distribution with a probability of one half.
| Slot | Paths of 256 | Chance | |---|--:|--:| | Edge (0 or 8) | 1 | 0.39% | | 1 or 7 | 8 | 3.13% | | 2 or 6 | 28 | 10.94% | | 3 or 5 | 56 | 21.88% | | Centre (4) | 70 | 27.34% |
The chances are per slot, so the two edges together come to 0.78%, one drop in 128. The middle three slots catch 71% of balls.
16 rows: a wider board with far longer edges
Doubling the rows to 16 gives 2¹⁶ = 65,536 paths and 17 slots. The extra rows make the edges much harder to reach, because there's still only one path to each of them.
| Slot | Paths of 65,536 | Chance | About 1 drop in | |---|--:|--:|--:| | Edge (0 or 16) | 1 | 0.0015% | 65,536 | | 1 or 15 | 16 | 0.024% | 4,096 | | 2 or 14 | 120 | 0.18% | 546 | | 3 or 13 | 560 | 0.85% | 117 | | 4 or 12 | 1,820 | 2.78% | 36 | | 5 or 11 | 4,368 | 6.67% | 15 | | 6 or 10 | 8,008 | 12.22% | 8.2 | | 7 or 9 | 11,440 | 17.46% | 5.7 | | Centre (8) | 12,870 | 19.64% | 5.1 |
One edge or the other comes up once in 32,768 drops, and the middle five slots take 79% of all drops. The typical spread grows only with the square root of the rows: the standard deviation is 1.4 slots on 8 rows and 2 slots on 16, while the number of slots nearly doubles. That's why balls look more tightly bunched on a big board.
What risk levels change
The row count and the risk level, Low, Medium or High, pick a payout table with one multiplier per slot. Every chance in the tables above stays the same whatever risk you choose. The ball doesn't know the risk setting; only the payouts move.
All the tables share a shape: symmetric, highest at the two edges and lowest in the middle. Low keeps the payouts close together, while High pushes value out to the edges and pays only a fraction of the stake in the middle. With the tables in use in October 2026, a 16-row drop on Low pays less than the stake only in the centre slot, about one drop in five. On High the five middle slots all pay less than the stake, about four drops in five, in exchange for edge slots worth around a thousand times the stake.
A table's average return is easy to work out: multiply each slot's multiplier by its chance and add them up. Risk changes how that return is spread across the slots, and the three tables for a given row count return about the same on average. The game page shows the house edge and the current multipliers, so you can do the sum yourself.
Rows, risk and your balance
More rows or higher risk barely change what Plinko costs on average; what they change is how bumpy the ride is. On High, a short session is mostly small returns from the middle, and an edge hit, if one comes, is what decides the total. Over many drops, results drift towards the table's average return, which is below 100%. House edge and RTP explains why the edge wins over many bets, and the gambler's fallacy covers why a long run of middle slots doesn't make an edge slot due: each drop uses new floats and doesn't remember the last.
A bet whose best slot would pay more than the game's maximum win is refused, so the tables with the biggest edge multipliers come with smaller maximum stakes.
Checking a drop
Every drop can be replayed from the seed pair. The first float decides row 1, the second decides row 2, and so on, with eight floats to each HMAC-SHA256(server seed, "client seed:nonce:k") block, so a 16-row drop uses two blocks. After you rotate your seed pair, the provably fair calculator redraws the path, and How to verify a provably fair bet shows the calculation by hand. The board itself is at Plinko.
